Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.32
URN: urn:nbn:de:0030-drops-126355
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12635/
Fomin, Fedor V. ; Golovach, Petr A. ; Panolan, Fahad ; Simonov, Kirill
Low-Rank Binary Matrix Approximation in Column-Sum Norm
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Abstract
We consider πβ-Rank-r Approximation over {GF}(2), where for a binary mΓ n matrix π and a positive integer constant r, one seeks a binary matrix π of rank at most r, minimizing the column-sum norm β π -πββ. We show that for every Ξ΅ β (0, 1), there is a {randomized} (1+Ξ΅)-approximation algorithm for πβ-Rank-r Approximation over {GF}(2) of running time m^{O(1)}n^{O(2^{4r}β Ξ΅^{-4})}. This is the first polynomial time approximation scheme (PTAS) for this problem.
BibTeX - Entry
@InProceedings{fomin_et_al:LIPIcs:2020:12635,
author = {Fedor V. Fomin and Petr A. Golovach and Fahad Panolan and Kirill Simonov},
title = {{Low-Rank Binary Matrix Approximation in Column-Sum Norm}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
pages = {32:1--32:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-164-1},
ISSN = {1868-8969},
year = {2020},
volume = {176},
editor = {Jaros{\l}aw Byrka and Raghu Meka},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12635},
URN = {urn:nbn:de:0030-drops-126355},
doi = {10.4230/LIPIcs.APPROX/RANDOM.2020.32},
annote = {Keywords: Binary Matrix Factorization, PTAS, Column-sum norm}
}
| Keywords: | Binary Matrix Factorization, PTAS, Column-sum norm | |
| Seminar: | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 11.08.2020 |
